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Physics 777 Plasma Physics and Magnetohydrodynamics (MHD). Instructor: Gregory Fleishman Lecture 9 . Large-Amplitude Waves and Discontinuities. 28 October 200 8. Plan of the Lecture. Simple Waves Nonlinear Waves, Solitons Discontinuities in the Plasma Shock Waves Strong Turbulence.
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Physics 777Plasma Physics and Magnetohydrodynamics (MHD) Instructor: Gregory Fleishman Lecture 9. Large-Amplitude Waves and Discontinuities 28 October 2008
Plan of the Lecture • Simple Waves • Nonlinear Waves, Solitons • Discontinuities in the Plasma • Shock Waves • Strong Turbulence
Section 1.1. Entropy simple waves If If & - arbitrary For other simple waves where
Section 1.3. Fast and slow simple waves If for some then for for all Consider simple case
Section 2. Nonlinear Waves, Solitons Korteweg – de Vries – Burgers Equation, which includes nonlinearity, dispersion, and dissipation as additive terms: where Burgers Equation Korteweg – de Vries (KdV) Equation
Section 2.1. Solitons Consider KdV Equation Seek solution
Necessary conditions: Case I For or result in
Rarefaction! Case II Jakobi elliptic function; - Cnoidal wave Chain of solitons
Upstream Downstream
Upstream Downstream & & &
Section 6. Homework • Complete Progress Reports on the research project. Include Introduction, the work done with plots, and plan for the remaining work. Be ready for brief presentation of the Progress Report.